Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/4292 2023 2023 Independent Researcher, Tokyo, Japan Takaaki Takaaki ajoykantidas@gmail.com Ajoy Kanti Das A Functorial Structure is defined as a covariant functor F : C → Set, assigning sets to objects and functions to morphisms, ensuring functoriality. In this paper, we introduce and formally define two new concepts: the HybridFunctorial Structure and the MultiFunctorial Structure. A HybridFunctorial Structure combines two functors on the same category, linked by a natural transformation, ensuring consistent pushforward compatibility. A MultiFunctorial Structure involves multiple functors indexed by a preorder, coherently related via natural transformations, forming compatible families with functorial consistency. 2026 2026 22 34 10.54216/PMTCS.060102 https://www.americaspg.com/articleinfo/40/show/4292